I'm no expert but I think of mulch as anything put on top of the soil to keep the moisture in and deter weed growth.
I think you can pretty much use anything you want - soaked newspaper, mushroom compost, wool, thick black plastic, an old carpet, and yes, grass clippings or bark. Some materials may have a downside - for instance I do know that sawdust can deplete nitrogen so mostly is not recommended as a mulch. I don't think bark has the same problem - being larger bits it breaks down more slowly.
I guess it's never essential - but is always a good idea, I think. In some circumstances it would certainly be strongly recommended, eg, somewhere with light soil and a lot of sun. However, if you are planting quick-growing plants thickly so that the plants will very soon shade out the soil with their foliage then maybe you could get away with not doing it.
My favourite mulch is a compost-based one; you get the added bonus of extra nutrients as it breaks down. Carpets and wool don't really break down and I'm not sure that cardboard or newspaper add much back to the soil. Black plastic certainly doesn't! However, the non-breaking-down ones are of course better at stopping weed regrowth.
HTH
Sally